Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic556 | C2 | semidirect |
| 2. #22581393 | C2 | direct (N × H) |
| 3. C2×#17984788 | C2 | semidirect |
| 4. C2×#17984786 | C2 | semidirect |
| 5. C2×#17984782 | C2 | semidirect |
| 11. C2×Dic556 | C22 | semidirect |
| 12. #17984788 | C22 | semidirect |
| 13. #17984786 | C22 | semidirect |
| 14. #17984782 | C22 | semidirect |
| 81. C2×C139 | #510 | semidirect |
| 83. C139 | C2×#510 | semidirect |
| 165. C2 | #22581393 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic556 | 2 |
| #22581393 | 2 |
| C2×#17984788 | 2 |
| C2×#17984786 | 2 |
| C2×#17984782 | 2 |
| C2×#135×C139 | 2 |
| C2×#510 | 139 |